The fact that I (a math teacher) learnt something new from this, means my students need to see it. Thumbs up my friend

This is literally the greatest explanation that I've ever heard. Beautifully animated and very straight to the point. The best video ever on this topic! You saved my life!😊

Some extra things that would be worth mentioning:
1) in the absence of linearity, the correlation itself may give you very little information. In some cases, data set with Corr = 0.9 might be closer to the one with Corr = 0, than to the other with Corr = 1. In other words, very weak trends (maybe not even worth mentioning) may give you high Corr value.
2) In random generated sets, certain degree of correlation may appear randomly, without a good reason.
3) Not only does correlation not imply causation, causation doesn't imply correlation as well. Take for example y = |x| for x \in [-1, 1]. Clearly y=f(x), yet Corr = 0.

I’m a statistics student in my final year of undergrad. I just felt like checking out a video on covariationnas we begin PCA. This is by far the most clear it has ever been explained, and so succinctly! Well done, I feel I can think about it more clearly now.

YouTube can't be serious that this video doesn't top their search result! Kudos to the channel. This video seriously deserves every compliment this world can offer. Keep up the great work thanks!

The animations helped me get an idea of what I was calculating for this long :) Maths is beautiful✨

3 hours until an econometrics midterm exam...

The video looks more like an animation exercise rather than an educational video. The formulas are explained but the intuition behind them is as opaque as before. A few videos from 3Blue1Brown could be a good reference for this channel.

this is the kind of explanation we need . 🙂

Super clear explanation!

It's crazy learning correlation without telling you about covariance

Have calculated this many times for portfolio risk reduction in class. Seeing an  animation clears it up again

well done.   great explaination.

Fantastic explanation, but one of the things that really sets this apart from some of the others I have seen is that you take time at the end to show the different values for different points. Really a great way to both help people visualize and check if they understood correctly.

what a beautiful animation, amazing video friend!

thank you so much for your crystal-clear explanation

amazing, will come back when I forget the concepts

great video! you really helped me to understand in 7 minutes what my proffesor could not in 1 hour! thanks!

Excellent video. Very intuitive and well explained! As someone who's both a student and a teacher of maths, I'm impressed from both angles!

I agree; this video was amazing!  And you are so right- the video, in the end, was so good to see what the values look like at different plot points.